The length of a rectangular garden is modeled by the expression x+2 and the width is modeled by the expression 2x-3. Write an expression for both perimeter and area of the rectangular garden in terms of x.

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It may help you to begin by drawing a picture to model this problem, labeling one side of the rectangle x+2 and the other side 2x-3 (although this step is not necessary).

1) Perimeter : The perimeter of a shape is the distance around the outside.  Generally you just add...

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It may help you to begin by drawing a picture to model this problem, labeling one side of the rectangle x+2 and the other side 2x-3 (although this step is not necessary).

1) Perimeter: The perimeter of a shape is the distance around the outside.  Generally you just add up the side lengths.  In the case of a rectangle, since the two lengths are the same and the two widths are the same, it can be shortened to the following formula:

`P=2l+2w`

All that needs to be done is to substitute the expressions given for length and width into the formula above:

`P=2(x+2)+2(2x-3)`

Then you just need to simplify the expression on the right by distributing and combining like terms:

`P=2x+4+4x-6`

`P=6x-2`

So the expression for the perimeter of the garden is 6x-2.

 

2) Area: The area of a shape is the amount of space inside of it (for which the formulas vary widely depending on the shape).  The formula for the area of a rectangle is

`A=l*w`

Once again, you just need to substitute the given expressions for length and width:

`A=(x+2)*(2x-3)`

In order to simplify, you will need to distribute the binomials (often call the FOIL method) and combine like terms:

`A=2x^2-3x+4x-6`

`A=2x^2+x-6`

So this is the expression for the area of the garden.

 

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